AU2021101917A4 - Intelligent prediction and multi-objective optimization control method for ground settlement induced by subway tunnel construction - Google Patents
Intelligent prediction and multi-objective optimization control method for ground settlement induced by subway tunnel construction Download PDFInfo
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Abstract
The present invention belongs to the technical field of subway tunnel construction
and discloses a method for intelligently predicting ground surface settlement induced
by the subway tunnel construction. the method includes the following steps: (a)
analyzing and decomposing high and low frequency signals of original settlement
monitoring data by means of a wavelet packet; (b) determining a parameter of a least
square support vector machine prediction model by means of a particle swarm
optimization algorithm, and fully extracting a variation trend of monitoring data by
means of the prediction model, and predicting a settlement signal of each node in real
time; (c) combining the settlement signals which are predicted individually in the high
and low frequency scope by means of a wavelet packet reconstruction technology to
obtain a final predicted value; and (d) proposing a performance indicator representing
a prediction capability of the model to verify the reliability and accuracy of the
prediction model. The present invention can extracted comprehensively and finely high
frequency and low frequency signals, separate strong signals and weak signals in the
high frequency and low frequency signals, can effectively avoid interference between
the strong signals and the weak signals, thereby improving the precision and reliability
for predicting the ground surface settlement induced by the subway tunnel
construction.
1/2
FIGURES OF THE SPECIFICATION
Decompose monitored
surface settlement values at
high and low frequencies
Constructing a training
sample
Using input and output
values of the training sampk
to calculate a kernel function
and a prediction model
Calculating a predicted valu4
of each node according to
the prediction model
Reconstructing the predicted
values of all nodes to obtain
a predicted value of ground
surface settlement
Calculating MAE and RMSE by
means of a monitored value of
the ground surface settlement
and the predicted value of the
around surface settlement
FIG. 1
Description
1/2
Decompose monitored surface settlement values at high and low frequencies
Constructing a training sample
Using input and output values of the training sampk to calculate a kernel function and a prediction model
Calculating a predicted valu4 of each node according to the prediction model
Reconstructing the predicted values of all nodes to obtain a predicted value of ground surface settlement
Calculating MAE and RMSE by means of a monitored value of the ground surface settlement and the predicted value of the around surface settlement
FIG. 1
Intelligent prediction and multi-objective optimization control method for
ground settlement induced by subway tunnel construction
The present invention belongs to the technical field of subway tunnel
construction, and more specifically, relates to a method for intelligently predicting
ground surface settlement induced by subway tunnel construction.
In the past few decades, the rapid development of big cities has triggered a
great demand for underground space development. Underground engineering
design and tunnel construction have become one of the most popular options in
the development of urban traffic. In a central area of a city, a tunnel is mostly
located under densely populated areas, and excavation engineering of a shallow
tunnel definitely produces horizontal and vertical soil surface movements in soft
foundations. Ground surface settlement induced by tunnel construction is a key
factor in assessment of a ground surface risk induced by the tunnel, especially in
densely populated urban areas. Therefore, evaluating, analyzing and controlling
the ground surface settlement induced by the tunnel is essential for taking
accurate and timely measures to avoid excessive ground surface settlement.
This is a key engineering issue to ensure safety of ground surface and
underground facilities during the subway tunnel construction.
At present, there are traditional time series analysis models such as ARMA
model and non-equal interval model for current analysis of a time course of ground surface settlement, as well as a modern advanced intelligent analysis model represented by a neural network method and a support vector machine.
Traditional analysis models cannot well analyze a complex nonlinear relationship
that changes over time; while an intelligent neural network algorithm can analyze
a nonlinear relationship. However, because a neural network is based on
empirical risk minimization, the neural network has high requirements for sample
quantity and quality. Although a Support Vector Machine (SVM) based on the
principle of structural risk minimization has a strong predictive ability for complex
nonlinear data of a small sample, a Least Square Support Vector Machine
(LSSVM) as a new extension method in a support vector machine greatly
improves a speed and a convergence accuracy of solving problems compared
with a conventional support vector machine. Zhang Huiyuan and Gu Hongjie et al
analyzed current-carrying fault trend prediction by means of the least square
support vector machine and proved the advantages in small-sample prediction.
However, because of complexity of a shield project, a data monitoring process is
easily affected by a construction environment. Ground surface settlement sample
data monitored in the project is not smooth, which makes a change trend not
obvious enough. Further, a weak trend in the change trend is easy to be ignored
in the prediction. Therefore, the intelligent prediction algorithm alone cannot well
meet prediction requirements of the ground surface settlement in a project.
Wavelet transformation is a time domain-frequency domain analysis method,
which has a good localization property in both a time domain and a frequency
domain. Wavelet signal decomposition can decompose a signal into a high frequency and a low frequency. The high frequency contains a weak signal in a data signal while the low frequency contains a strong signal. This separates the strong and weak signals and effectively avoids a mutual interference of the strong and weak signals. Therefore, the use of wavelet signal decomposition in the intelligent algorithm prediction helps fully extract a trend of a change in the monitoring data and improve forecast accuracy. Yang Jun and Hou Zhongsheng et al decomposed the data signal by means of wavelet analysis and predicted rail traffic passenger flow by means of the support vector machine, which effectively improves prediction accuracy. Although Yang Jun et al have carried out research on the combined application of the two no scholars have conducted research on the application in the field of subway engineering. In addition, Yang Jun et al.'s research only used the wavelet decomposition to decompose the signal instead of using wavelet packet analysis that can fully and finely decompose the signal.
In the least square support vector machine prediction, no more accurate and
advanced intelligent algorithm is used to set a parameter of the model.
In view of the forgoing defects or improvement needs in the prior art, the
present invention provides a method for intelligently predicting ground surface
settlement induced by subway tunnel construction. By constructing a ground
settlement prediction model in a tunnel construction environment, the method
solves a technical problem of accurate prediction of real-time and dynamic
ground surface settlement under tunnel construction conditions and reduces the
adverse effects of the ground surface settlement during the tunnel construction.
To achieve the above objective, according to one aspect of the present
invention, a method for intelligently predicting ground surface settlement induced
by subway tunnel construction is provided, and includes the following steps:
(a) first using a wavelet packet function to decompose a monitored ground
surface settlement value sO(t) at a high frequency and a low frequency to obtain
a low frequency nodepI(t) and a high frequency node A'(t of a first layer, and
then continuing to decompose the low frequency node pft and the high
frequency node A'(t of the first layer at the high frequency and the low
frequency, respectively, obtaining a node of a second layer until the
decomposition is ended to a m-th layer, the m-th layer has 2m nodes, and the i-th
node of the m-th layer has a node signal pi(t) at time t, where i=0, 1, 2,..., 2m-1,
t=1, 2,...,L,...,n, t is the sampling time, m and n are all positive integers greater
than 1;
(b) constructing a prediction model by means of the first L of the node
signals p(t)whose t takes a value of 1 to L;
(b1) The first L node signals p'(t)' constitute a total of L-q training samples,
where the node signal at q consecutive moments is used as an input value, the
node signal at the next moment is used as a preset output value, and there are
n-q training samples in total when a value range of t is 1-n;
(b2) substituting an input value of each of the L-q training samples into a
prediction model composed of a kernel function, and calculating an output value
of each sample, equally constructing an equation by means of a calculated output value and a preset output value, and calculating a parameter of the kernel function by means of an optimization algorithm to obtain a prediction model;
(b3) substituting the input value of each of the n-q training samples into the
prediction model to obtain the corresponding output value, '"M(q+1)
p; (q+2)' ,(n-1)' p(n)', and combine it with first q moments of the node
signal Pm(t) as follows to obtain a predicted node signalP(t)
p'4(t)'* ={p',(1), p'(2),L ,p',(q), p'(q+1)', p'(q+2)',L,p',(n)'
(c) reconstructing the predicted signal Ptfi(0 according to the wavelet
packet function based on the following expression to obtain the ground surface
settlement value to be predicted, where Pi (t) is the function of predicting the
node signal at the i-th node in the m-th layer, and P*(0 is a predicted ground
surface settlement value, the value range of j is 1-m,
p'. (t)' = p '+- (t)'*+p ' (t)' 2i t =1,2.n |p*(t)= pt'
(d) calculating an average absolute error MAE and a root mean square error
RMSE, which are used to analyze the prediction effect of the prediction model.
Further, preferably, in step (b2), the optimization algorithm preferably adopts
a particle swarm optimization algorithm, and the condition for stopping
optimization is that there is a difference E!0.05 between the calculated output
value and the preset output value.
Further, preferably, in step (b2), the kernel function K(x, xt) preferably adopts
a radial basis kernel function, which is expressed as follows, where a is a width
of the radial basis function, x is a input value, and xt is a central value of a radial
basis function:
K(x,x,)= exp K(x-x)(x-xY)" - '2 , t =1,2,...,n 2
Further, preferably, in step (b2), the prediction model y(x) preferably adopts
a least square support vector machine prediction model, which is based on the
following expressions, where at and b are constant coefficients,
y(x)= a,K(x,x,)+b
Further, preferably, in step (d), the average absolute error (MAE) and the
root mean square error (RMSE) are preferably performed using the following
expressions:
1 A1E=-Y sO(t)-p*(t)x100%, t=1,2,...,n n
RM E sxt- *t x100%, t =1, 2,..., n
In general, compared with the prior art, the forgoing technical solutions
conceived by the present invention can achieve the following beneficial effects:
1. By organically integrating wavelet packet decomposition, reconstruction
technology, least square support vector machine technology, a particle swarm
optimization algorithm, etc., the present invention can accurately predict daily
settlement and cumulative settlement of ground deformation induced by subway tunnel construction in real time. Further, the requirements for training samples are low, and higher prediction accuracy can be obtained under the premise of a small sample, and the problems of high computational complexity and slow training speed can be avoided.
2. The present invention uses the wavelet packet decomposition to
decompose original detection data according to a high frequency and a low
frequency. The high frequency contains a weak signal in a data signal while the
low frequency contains the strong signal, which makes the strong and weak
signals separate and effectively avoids a mutual interference of weak and strong
signals. This hence can fully extract a trend of a change in monitoring data and
improve prediction accuracy;
3. The present invention uses a radial basis kernel function (RBF) as a
kernel function to accurately extract a local change trend of ground surface
settlement monitoring. Compared with other kernel functions, the RBF function
has a strong local predictive ability. In addition, compared with other kernel
functions, the only parameters that need to be set for the RBF function are a
kernel function parameter 9 and a regularization parameter C;
4. In the present invention, the particle swarm optimization algorithm in the
intelligent optimization algorithm is used to determine the parameter of the kernel
function. Compared with other genetic algorithms, the algorithm is simpler and
more effective in coding and optimization strategies than genetic algorithms;
5. Compared with other an existing BP neural network method and an
existing RBF neural network prediction method, the present invention uses a least square support vector machine prediction method whose prediction result has higher accuracy and whose error level is much lower than the other two methods.
FIG. 1 is a flowchart of an intelligent prediction method constructed
according to a preferred embodiment of the present invention;
FIG. 2 is an application effect diagram of a subway tunnel construction
project constructed according to a preferred embodiment of the present
invention.
In order to make the objectives, technical solutions and advantages of the
present invention clearer, the following further describes the present invention in
detail with reference to the accompanying drawings and embodiments. It should
be understood that the specific embodiments described herein are only used to
explain the present invention, but not to limit the present invention. In addition,
the technical features involved in various embodiments of the present invention
described below can be combined with each other as long as the technical
features do not conflict with each other.
FIG. 1 is a flowchart of an intelligent prediction method constructed
according to a preferred embodiment of the present invention. As shown in FIG.
1, this embodiment provides a method for intelligently predicting ground surface
settlement induced by subway tunnel construction by means of wavelet packet decomposition, reconstruction technology and least square support vector machine technology, specifically including the following steps:
(1) Decomposing a wavelet packet
decomposing a signal by means of wavelet packet decomposition
technology, assuming that the signal is decomposed into m layers. A
decomposition process first uses a wavelet packet function to decompose
original data so(t) at a high frequency and a low frequency to obtain a low
frequency node pi(t) of a first layer and a set of high frequency nodesp1 (t),
and then continue to perform high frequency and low frequency decomposition
for PI(t) and p(t) to obtain nodes of a second layer until the decomposition is
ended to a m-th layer. Then a wavelet packet decomposition tree T is finally
obtained, in which there are 2m nodes in the m-th layer, and the nodes are
numbered by means of nd=m+1,m+2,L ,m+2' in turn. Then the nodes in the
m-th layer of the decomposition tree T are respectively reconstructed to obtain a
node signal real-time frequency data sequencet(t)(i=,1,2,L,2' -1)
(2) predicting a Least Square Support Vector Machine (LSSVM) of the node.
The particle swarm optimization algorithm is used to optimize and determine
a parameter of a prediction model of the least squares support vector machine.
Through the prediction model, a trend of a change in monitoring data is fully
extracted and the ground surface settlement is predicted. There are n data in the
nodedata sequence p (t)(i= 0,1, 2,L, 2' -1;t =1, 2L , n) analyzed by wavelet
packet, the first L data are used to train LSSVM, and the remaining K data are predicted by LSSVM after training. LSSVM prediction is mainly divided into the following sub-steps:
(I) determining the sample. Constructing a sample set of n data in the time
series. Because a LSSVM unit is a multi-input single output, every q data are set
as one input, and the data at the next moment is used as an output value. A data
input and output structure is shown in the table. The samples constructed by the
first L data are used as training samples, and there are a total of L-q training
samples as shown in Table 1.
Table 1: Table for LSSVM prediction input and output samples
Sample number Input data Output Data 1 (i(1),pu' (2),L u,(q)} ',(q+1)'
L-Q {p'(L - q), p'(L - q +1),L p'(L - 1)} p L'
n-q (p(n -q),p' (n -q+1),L p'(n -1)) (p(n)')
(II) Determining a kernel function and an important parameter. First selecting
the kernel function, wherein a correct selection of the kernel function depends on
the characteristics of an actual problem. Because of an obvious local variation of
the ground surface settlement monitoring data, the prediction needs to accurately
extract a local change trend, and the radial basis kernel function (RBF) has the
strongest local prediction ability compared to other kernel functions, and the only
parameters that needs to be set relative to other kernel functions are a kernel
function parameter 9 and a regularization parameter C. therefore, BRF is
selected as the kernel function. The kernel function parameter a and the
regularization parameter C are then determined. Scholars have proposed many methods for determining the parameters. The intelligent optimization algorithm is a new idea and verified to be effective. The particle swarm optimization algorithm can be applied to all the occasions where a genetic algorithm can be applied, and is simpler and more effective than the genetic algorithm in coding and optimization strategies. The particle swarm optimization algorithm is used to globally optimize the kernel function parameter 9 and the regularization parameter C to determine the parameters. The expression of the radial basis kernel function is as follows, where c is a width of the radial basis kern el function, x is an input value, and xt is a central value of the radial basis function,
K(x-x)(x-x)" , K(x,x,)= exp - '2 2 t =1,2,...,n
(III) training the model First setting the determined parameters, and then
inputting the training sample composed of the first L data in an i-th wavelet until
the training result meets the requirements, wherein a LSSVM model is obtained
by means of the kernel function parameter o and the regularization parameter C.
The expression of the model is as follows, where at and b are constant
coefficients,
y(x) a,K(x,x,)+b t-1
(IV) predicting the model Inputting the input data in Table 1 into the trained
LSSVM model to obtain output data, that ispt(q+1,i(q+2)',L n-1
and forming a prediction sequence P,(t) '={p(1)', (2), (- ( with the first q data in the data after noise reduction, and then obtaining 2m prediction sequences t = 0,1,2,3L 2' -1)in turn.
(3) reconstructing a wavelet packet
Through wavelet packet signal recombination technology, a settlement
signal separately predicted in high-frequency and low-frequency scopes are
synthesized to obtain a final predicted value of the ground surface settlement
induced by the subway tunnel construction. At this stage, the prediction
sequence is reconstructed to predict the ground surface settlement induced by a
tunnel. In the training set and the test set, an i-th decomposition sequence can
obtain the predicted value of the ground surface settlement induced by the
tunnel. Being similar to a first stage of a decomposition process, all
decomposition sequences can be reconstructed after classification, as shown in
the following formula, whereP,,(t) is a function of predicting the signal of the
node at the i-th node in the m-th layer, and P*(t is the predicted value of the
ground surface settlement. And the value range of j is 1-m,
p' (t' 2=p ' (t'* p ' (t)*
' t =1,2.n
(4) analyzing a model error
A performance indicator that characterizes a predictive ability of the model is
put forward to verify reliability and accuracy of the prediction model, and
applicability in the prediction of the ground surface settlement in the subway
tunnel construction. Two indicators of a Mean Absolute Error (MAE) and a Root
Mean Square Error (RMSE) are proposed to analyze a prediction effect of the
prediction model. An average absolute error describes an average size of the
forecast error distribution. When the average absolute error is zero, the model
performs well, and when the average absolute error is greater than 0, it reflects
that the predicted value is different from an observed value. The root mean
square error describes a variance of the predicted and observed distribution
errors. When the root mean square error is zero, it means that the model can
accurately predict the observed value. When the root mean square error is
greater than zero, the model has an error. The average absolute error measures
prediction accuracy of the model, and the root mean square error reflects
prediction stability of the model. The average absolute error and the root mean
square error can be calculated by the following two formulas respectively.
A1E=-sO(t)-p*(t)x100%, t=1,2,...,n n
RMSE= YsO(t)-p*(t) x100%, t=1,2,...,n
As shown in FIG, 2, the present invention is actually applied in a subway
tunnel construction project. FIG. 2(a) shows the surface settlement observed by
monitoring points DK26460 and DK26580 during the tunnel construction from
April 13, 2015 to June 11, 2015. Taking monitoring data of the monitoring point
DK26460 as an example, FIG. 2(b) shows actual monitoring data of the
monitoring point DK26460 decomposed into four layers by means of the wavelet
packet decomposition technology; FIG. 2(c) shows settlement prediction values
predicted in different scopes of the high and low frequencies after a data sample of the monitoring point DK26460 are trained by the least square support vector machine. FIG. 2(d) shows a final predicted settlement value after prediction data of the monitoring point DK26460 is reconstructed after the wavelet packet. Table
2 shows comparison results of prediction errors of the least squares support
vector machine used in the present invention and the BP neural network and
RBF neural network prediction methods. The results show that an error level of
the prediction method proposed by the present invention is much lower than the
other two prediction methods. Prediction accuracy and reliability of the present
invention is greatly improved.
Table 2 Comparison results of prediction errors using different methods
Monitoring BP neural RBF neural Least square support vector The present ont network network machine invention points MAE RMSE MAE RMSE MAE RMSE MAE RMSE DK26460 0.3984 0.2496 0.3669 0.2535 0.3931 0.2754 0.1023 0.0218 DK26580 0.3201 0.2271 0.3640 0.1882 0.2068 0.0967 0.0989 0.0256 Average 0.3593 0.2381 0.3655 0.2209 0.3000 0.1861 0.1006 0.0237 values
The person skilled in the art easily understands that the forgoing are only the
preferred embodiments of the present invention and are not intended to limit the
present invention. Any modification, equivalent replacement and improvement
made within the spirit and principle of the present invention shall be included
within the protection scope of the present invention.
Claims (5)
1. A method for intelligently predicting ground surface settlement induced by
subway tunnel construction, comprising the following steps:
(a) first using a wavelet packet function to decompose a monitored ground
surface settlement value sO(t) at a high frequency and a low frequency to obtain
a low frequency nodepI(t) and a high frequency node A'(t of a first layer, and
then continuing to decompose the low frequency node p1(t) and the high
frequency node A'(t of the first layer at the high frequency and the low
frequency, respectively, obtaining a node of a second layer until the
decomposition is ended to a m-th layer, the m-th layer has 2m nodes, and the i-th
node of the m-th layer has a node signal pi(t) at time t, where i=0, 1, 2,..., 2m-1,
t=1, 2,...,L,...,n, t is the sampling time, m and n are all positive integers greater
than 1;
(b) constructing a prediction model by means of the first L node signals
p whose t takes a value of 1 to L;
(b1) The first L node signals p'(t)' constitute a total of L-q training samples,
where the node signal at q consecutive moments is used as an input value, the
node signal at the next moment is used as a preset output value, and there are
n-q training samples in total when a value range of t is 1-n;
(b2) substituting an input value of each of the L-q training samples into a
prediction model composed of a kernel function, and calculating an output value
of each sample, equally constructing an equation by means of a calculated output value and a preset output value, and calculating a parameter of the kernel function by means of an optimization algorithm to obtain a prediction model;
(b3) substituting the input value of each of the n-q training samples into the
prediction model to obtain the corresponding output value, '"M(q+1)
p; (q+2)' ,(n.p -1)' p(n)', and combine it with first q moments of the node
signal Pm(t) as follows to obtain a predicted node signalP(t)
p'4(t)'* ={p',(1), p'(2),L ,p',(q), p'(q+1)', p'(q+2)',L,p',(n)'
(c) reconstructing the predicted signal Ptfi(0 according to the wavelet
packet function based on the following expression to obtain the ground surface
settlement value to be predicted, where Pi (t) is the function of predicting the
node signal at the i-th node in the m-th layer, and P*(0 is a predicted ground
surface settlement value, the value range of j is 1-m,
2' , t = 1,2,. |p*(t)= pt'
(d) calculating an average absolute error MAE and a root mean square error
RMSE, which are used to analyze the prediction effect of the prediction model.
2. The method for intelligently predicting the ground surface settlement
induced by the subway tunnel construction according to claim 1, wherein in step
(b2), the optimization algorithm preferably adopts a particle swarm optimization
algorithm, and the condition for stopping optimization is that there is a difference
E!0.05 between the calculated output value and the preset output value.
3. The method for intelligently predicting the ground surface settlement
induced by the subway tunnel construction according to claim 1 or 2, wherein in
step (b2), the kernel function K(x, xt) preferably adopts a radial basis kernel
function, which is expressed as follows, where a is a width of the radial basis
function, x is a input value, and xt is a central value of a radial basis function:
K(x-x)(x-x)" , K(x,x,)= 2 2 ' t=1,2,...,n
4. The method for intelligently predicting the ground surface settlement
induced by the subway tunnel construction according to any one of claims 1 to 3,
wherein in step (b2), the prediction model y(x) preferably adopts a least square
support vector machine prediction model, which is based on the following
expressions, where at and b are constant coefficients,
y(x)= a,K(x,x,)+b
5. The method for intelligently predicting the ground surface settlement
induced by the subway tunnel construction according to any one of claims 1 to 4,
wherein in step (d), the average absolute error (MAE) and the root mean square
error (RMSE) are preferably performed using the following expressions:
A1E=-Y sO(t)-p*(t)x10%, t=1,2,...,n n RMS - o W- i (0
RM E sxt-1 *t x100%, t =1, 2,..., n
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| CN113806843A (en) * | 2021-09-01 | 2021-12-17 | 北京住总集团有限责任公司 | Deformation analysis system and method based on dynamic fluctuation of bottom of sedimentation tank |
| CN114372314A (en) * | 2022-01-17 | 2022-04-19 | 上海市基础工程集团有限公司 | Method for predicting ground settlement caused by pressure reduction and precipitation |
| CN114413832A (en) * | 2021-12-02 | 2022-04-29 | 中国通信建设第三工程局有限公司 | Road monitoring system and method based on optical fiber sensing |
| CN116226958A (en) * | 2022-12-08 | 2023-06-06 | 同济大学 | Maintenance strategy optimization method for longitudinal settling tank of rail transit tunnel |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113806843A (en) * | 2021-09-01 | 2021-12-17 | 北京住总集团有限责任公司 | Deformation analysis system and method based on dynamic fluctuation of bottom of sedimentation tank |
| CN113806843B (en) * | 2021-09-01 | 2024-05-31 | 北京住总集团有限责任公司 | Deformation analysis system and method based on dynamic fluctuation of sedimentation tank bottom |
| CN114413832A (en) * | 2021-12-02 | 2022-04-29 | 中国通信建设第三工程局有限公司 | Road monitoring system and method based on optical fiber sensing |
| CN114413832B (en) * | 2021-12-02 | 2023-12-15 | 中国通信建设第三工程局有限公司 | Road monitoring system and method based on optical fiber sensing |
| CN114372314A (en) * | 2022-01-17 | 2022-04-19 | 上海市基础工程集团有限公司 | Method for predicting ground settlement caused by pressure reduction and precipitation |
| CN116226958A (en) * | 2022-12-08 | 2023-06-06 | 同济大学 | Maintenance strategy optimization method for longitudinal settling tank of rail transit tunnel |
| CN116226958B (en) * | 2022-12-08 | 2023-11-24 | 同济大学 | Maintenance strategy optimization method for longitudinal settling tank of rail transit tunnel |
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